Petulance is whininess and irritability. Your least favorite thing about the kids you babysit might be their petulance.
The noun petulance is the quality of being fretful, complaining, petty, or generally cranky. It's not a pleasant characteristic — it's almost always described negatively, like when you talk about the childishness and petulance of your constantly whining boss or the petulance of a hotel guest who complains about the pillows being too fluffy. Petulance comes from the Latin petulantia, which means insolence or immodesty.